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Spin–vibronic coherence drives singlet–triplet conversion


Design-specific control over the transitions between excited electronic states with different spin multiplicities is of the utmost importance in molecular and materials chemistry1,2,3. Previous studies have indicated that the combination of spin–orbit and vibronic effects, collectively termed the spin–vibronic effect, can accelerate quantum-mechanically forbidden transitions at non-adiabatic crossings4,5. However, it has been difficult to identify precise experimental manifestations of the spin–vibronic mechanism. Here we present coherence spectroscopy experiments that reveal the interplay between the spin, electronic and vibrational degrees of freedom that drive efficient singlet–triplet conversion in four structurally related dinuclear Pt(II) metal–metal-to-ligand charge-transfer (MMLCT) complexes. Photoexcitation activates the formation of a Pt–Pt bond, launching a stretching vibrational wavepacket. The molecular-structure-dependent decoherence and recoherence dynamics of this wavepacket resolve the spin–vibronic mechanism. We find that vectorial motion along the Pt–Pt stretching coordinates tunes the singlet and intermediate-state energy gap irreversibly towards the conical intersection and subsequently drives formation of the lowest stable triplet state in a ratcheting fashion. This work demonstrates the viability of using vibronic coherences as probes6,7,8,9 to clarify the interplay among spin, electronic and nuclear dynamics in spin-conversion processes, and this could inspire new modular designs to tailor the properties of excited states.

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Fig. 1: System description and outline of experiments.
Fig. 2: Chirp dependence, dephasing dynamics and lineshape analyses of vibrational coherences.
Fig. 3: Spectral Fourier filtering and nonlinear least-squares fitting reveals a hidden intermediate state.
Fig. 4: Vibrational coherence dynamics during ISC.

Data availability

Source data are provided with this paper.


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The National Science Foundation supported this collaborative research through grants CHE-1955806 (to S.R. and L.X.C.) and CHE-1955795 (to S.K. and F.N.C.). The US Department of Energy, Office of Science and Office of Basic Energy Sciences, Ultrafast Science Initiative, provided support through contract number DE-AC02-06CH11357 (to N.P.W. and L.X.C.).

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Authors and Affiliations



S.R. conceived and led the project, designed and performed the experiments, analysed the data and led the preparation and writing of the manuscript; N.P.W. contributed to designing and performing the experiments; S.K. synthesized and structurally characterized the molecules; and F.N.C. and L.X.C. contributed to conceiving the work and designing the experiments, obtained funding, supervised the research and contributed to writing the manuscript. All authors contributed to the preparation and writing of the manuscript.

Corresponding authors

Correspondence to Felix N. Castellano or Lin X. Chen.

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Extended data figures and tables

Extended Data Fig. 1 Chirp-dependent vibrational wavepacket dynamics in Pt2.

Integrated Fourier transforms of Pt2 in THF solvent obtained from the BBPP measurements under five different excitation pulse conditions. The excitation pulses used in measuring these datasets were Transform-limited (TL) pulses of duration (~7-fs) or positively chirped (PC1 and PC2) with a GVD of around 60 and 120 fs2/mm and negatively chirped (NC1 and NC2) pulses with a GVD of around −60 and −120 fs2/mm respectively. These FT bands clearly show a peak at 112 cm−1 frequency as well as a broad relatively less intense band in its high frequency region. These FT spectra are intensity normalized to the peak amplitude at 112 cm−1 band.

Extended Data Fig. 2 2DES beat-maps of ground and excited state wavepackets in Pt1.

Contour plots of 2DES beat-maps of 107 (a) and 147 cm−1 (b) Fourier transform bands of Pt1 in tetrahydrofuran solvent. The amplitude of the 107 cm−1 FT band in this excitation-detection correlation map (beat-map) is distributed in a manner that the contour mostly peaks at the excitation and detection frequency close to the ground state bleach, indicative of its ground state origin. For 147 cm−1 FT band, the amplitude of the beat-map is shifted to lower energy along the detection frequency axis relative to the 107 cm−1 band, indicative of its origin from the stimulated emission signal, which in turn assigns this FT band to the 1MMLCT excited state. These 2DES beat-maps are obtained by extracting the oscillatory signal in the time-domain from the electronic population signal using a fitting procedure, followed by Fourier transforming the residual oscillations. The selective Fourier transform bands (107 cm−1 and 147 cm−1 in this case) are filtered and their amplitude is plotted in the 2DES excitation-detection frequency correlation map.

Extended Data Fig. 3 Multipeak fitting of the Fourier transform lineshapes of Pt1 and Pt2.

Multipeak fitting procedure applied to the FT bands of the Pt1 (a) and Pt2 (b) complexes to retrieve the bandwidth and peak frequency of the overlapping bands. The red traces are raw FT traces, and the blue traces are the fitted traces using two Lorentzian functions. This fitting procedure was extended to all the five excitation conditions namely transform limited pulse, two positively chirped pulse cases, and two negatively chirped pulse cases. The red Lorentzian bands at the bottom of each panel with shaded background are the deconvoluted fits to the overlapping bands. This multipeak fitting procedure successfully resolved the width and peak frequency of the broad, less intense band on the high frequency region of 112 cm−1 band in Pt2. Apparently, the intensity of this broad feature in Pt2 is too weak in the case of negatively chirped excitation pulse to be resolved clearly. All the fitting parameters from this multipeak fitting procedure are tabulated in Extended Data Table 1 below.

Extended Data Fig. 4 Fourier transforms depicting the high-frequency modes in Pt1-Pt4.

The Fourier transform spectra of all four Pt complexes in THF solvent in the range 1100–1800 cm−1 are shown. The FT spectrum of the THF solvent is also shown for comparison. These FT spectra are obtained from the 2DES measurements. Most of the peaks in this spectral region are primarily the solvent Raman peaks. Additionally, we can identify peaks that belong to dinuclear platinum complexes. For Pt2 and Pt4, two peaks at 1243 and 1305 cm−1 frequencies can be found; for Pt1 and Pt3, 1262 and 1320 cm−1 frequencies are found. Since Pt2 and Pt4 share the same ligand and Pt1 and Pt3 also share the same ligand, it indicates that these frequencies predominantly originate from ligand sites.

Extended Data Fig. 5 2DES beat-maps of the main vibrational wavepacket in Pt3 and Pt4.

Contour plots of 2DES beat-maps of 145 (a) and 148 cm−1 (b) Fourier transform bands of Pt3 and Pt4 complexes respectively. The amplitude of the two FT bands in these excitation-detection correlation maps (beat-maps) are distributed in a manner that the contours peak at the excitation and detection frequency coordinates that match with the triplet absorption signal coordinates, suggesting that these wavepackets originate in the triplet state.

Extended Data Fig. 6 Chi-square test of the vibrational wavepacket lineshapes in Pt1 and Pt4.

Chi-square test (χ2) of the Fourier transform lineshape fitting is shown. Chi-square is a statistical test used to examine the difference between categorical values from a random sample to judge the goodness of fit between expected and observed results. In simpler terms, the smaller the chi-square value, the greater the probability that there is an insignificant difference between the observed and the fit results. (ab) Pt1 Fourier transform band in the region from 0–300 cm−1 corresponding to ωprobe = 18,200 cm−1 is fitted with a single Lorentzian and Gaussian lineshapes. The χ2 value for Lorentzian fit is 0.017, which is ~9 times smaller than the χ2 value of 0.156 for Gaussian fit, indicating that Lorentzian fit is the best fit (cd) Pt4 Fourier transform band from 0–300 cm−1 corresponding to ωprobe = 17,000 cm−1 is fitted with two Lorentzian and Gaussian lineshapes. The χ2 value for Lorentzian fit is 0.141 which is ~7 times larger than the χ2 value of 0.019 for Gaussian fit. When the data is constrained to be fitted only for the peak at 148 cm−1 (e-f) the χ2 value for Lorentzian fit is 0.116 which is ~10 times larger than the χ2 value of 0.011 for Gaussian fit. Thus, confirming that Gaussian fit is the best fit for the Pt4 data.

Extended Data Fig. 7 Fourier transform maps showing distribution of wavepacket amplitude in Pt1-Pt4.

Broadband pump probe Fourier transform maps of Pt1-Pt4 in THF solvent. These FT maps are generated by removing electronic population signal from the total BBPP signal and then Fourier transforming the residual oscillations. These resultant FT bands correspond to the frequency of the vibrational modes coupled to the electronic transitions. In the Pt1 and Pt2 complexes, the higher frequency Fourier transform band at ~150 cm−1 frequency is shifted to the lower probe frequency than the band at ~110 cm−1 frequency, indicative of the origin of former band from the stimulated emission signal and the origin of the latter band from the ground state bleach signal. In the Pt3 and Pt4 complexes, a prominent band is observed at ~150 cm−1 frequency with a broad and less intense feature on its low-frequency region.

Extended Data Fig. 8 Depiction of amplitude node associated with the vibrational wavepackets in Pt3 and Pt4.

Phase change in the oscillations- indicated by the appearance of a node, as a function of probe frequency along the waiting time is shown for Pt3 and Pt4. The clarity of the node is enhanced by performing inverse Fourier filtering procedure of the 145 cm−1 in Pt3 and 148 cm−1 in Pt4 modes using a super-Gaussian window. This window explicitly extracts the wavepacket oscillations corresponding to these frequencies, which are otherwise superimposed by other frequency wavepackets. The nodes can be seen at ωprobe = ~16,300 cm−1 probe frequency for Pt3 and ωprobe = ~15,000 cm−1 for Pt4, and as the waiting time increases the position of node shifts towards lower probe frequency, typical of time-dependent energy lowering of the corresponding electronic state. The position of the node is in the same spectral region where triplet absorption peaks, clearly indicating that this wavepacket modulates the electronic signal of the triplet 3MMLCT state. The colour scale in these oscillation maps represent wavepacket amplitude oscillating about mean zero.

Extended Data Fig. 9 Chirp-dependent vibrational wavepacket dynamics in Pt3 and Pt4.

Integrated Fourier transform spectra of Pt3 and Pt4 complexes obtained by integrating the Fourier transform maps at all the probe frequencies in the BBPP data. The five Fourier transform spectra shown in each plot correspond to five different excitation conditions differing in the chirp of the excitation pulse namely Transform limited pulses (TL), positively chirped pulses of GVD around 60 fs2/mm, positively chirped pulses of GVD around 120 fs2/mm, negatively chirped pulses of GVD around −60 fs2/mm, and negatively chirped pulses of GVD around −120 fs2/mm. Plots (a) and (b) show the original and normalized Fourier transform spectra of Pt3 and (c) and (d) show the original and normalized spectra for Pt4 complex. In (b) and (d), the spectra are normalized to the intense peak of 145 and 148 cm−1 frequencies respectively. The shaded area in each plot represents the broad and less-intense feature in the lower frequency region with respect to the main intense band. The absence of any correlation in the peak intensity as a function of chip of the laser pulse indicates that this intense peak most likely originates from the triplet manifold instead of the singlet manifold.

Extended Data Fig. 10 Windowed Fourier transform of a representative trace in Pt4.

The Fourier transform of a representative oscillatory trace (ωprobe = 17,000 cm−1) windowed from t2 = 500 fs to 3 ps in Pt4 is shown. The initial 500-fs of the data were cut off intentionally to showcase that the oscillations corresponding to the broad Fourier transform band to the lower frequency of 148 cm−1 band dephase at a rapid rate. The Fourier transform band shows only sharp peak at ~148 cm−1 frequency.

Extended Data Fig. 11 Oscillation maps of filtered vibrational wavepackets in Pt3 using spectral filtering.

Fourier filtering procedure applied to the BBPP data of Pt3 complex. The procedure involves filtering out a Fourier transform band of interest by using a super-Gaussian window. The filtered Fourier transform band is then inverse-Fourier transformed to isolate the time-domain signal of the selective band from all other bands in the Fourier transform spectrum. The filter is initially applied to a single oscillatory trace and then extended to the full pump probe dataset. The extracted time-domain signal of a selected Fourier transform band as a function of probe frequency then shows the spectral and time-domain distribution of the amplitude of a particular mode. In this figure, the filter is first chosen to be broad enough to accommodate the whole FT band (a) as shown by the shaded area in the top panel. The filtered FT band is then inverse Fourier transformed and overlayed on the original oscillatory trace to show the matching of the original and filtered trace in the middle panel. The map of the oscillations as a function of probe frequency and time (lower panel) to demonstrate how the amplitude of a particular wavepacket is distributed. We notice that with a broad filter, two components can be observed in the map based on the distribution of the amplitude. When the filter is tightened to select the 145 cm−1 mode only (b) the oscillation amplitude first grows in time up to ~ 1ps and then decay over >3-ps window. Moving the filter to select the broad and less intense FT band only (c) shows that the oscillations dephase within a time-window of ~500-fs. The dephasing time of these oscillations corroborates with the growth time of the 145 cm−1 mode oscillations. We also selectively filtered out the FT band at 110 cm−1 frequency (d) that peaks out of the broad and less intense band. These oscillations survive for ~>1-ps time-window.

Extended Data Table 1 Fitted parameters of the vibrational wavepacket lineshapes in Pt1-Pt4

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Rafiq, S., Weingartz, N.P., Kromer, S. et al. Spin–vibronic coherence drives singlet–triplet conversion. Nature 620, 776–781 (2023).

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